Related papers: Uncertainty-Aware Principal Component Analysis

Principal Component Analysis (PCA) is a commonly used tool for dimension reduction in analyzing high dimensional data; Multilinear Principal Component Analysis (MPCA) has the potential to serve the similar function for analyzing tensor…

We study the fairness of dimensionality reduction methods for recommendations. We focus on the fundamental method of principal component analysis (PCA), which identifies latent components and produces a low-rank approximation via the…

Sequential or online dimensional reduction is of interests due to the explosion of streaming data based applications and the requirement of adaptive statistical modeling, in many emerging fields, such as the modeling of energy end-use…

We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a $p$-variate time series such that the transformed series is segmented…

In many scientific disciplines, the features of interest cannot be observed directly, so must instead be inferred from observed behaviour. Latent variable analyses are increasingly employed to systematise these inferences, and Principal…

Hyperspectral optical imaging provides rich spectral information for estimating continuous environmental and material parameters; however, its high dimensionality and strong feature correlation pose significant challenges for machine…

Principal Component Analysis is a key technique for reducing the complexity of high-dimensional data while preserving its fundamental data structure, ensuring models remain stable and interpretable. This is achieved by transforming the…

Dimensionality reduction algorithms like principal component analysis (PCA) are workhorses of machine learning and neuroscience, but each has well-known limitations. Variants of PCA are simple and interpretable, but not flexible enough to…

We consider the problem of decomposing a large covariance matrix into the sum of a low-rank matrix and a diagonally dominant matrix, and we call this problem the "Diagonally-Dominant Principal Component Analysis (DD-PCA)". DD-PCA is an…

Principal Component Analysis (PCA) is a classical method for reducing the dimensionality of data by projecting them onto a subspace that captures most of their variation. Effective use of PCA in modern applications requires understanding…

Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal,…

Principal component analysis (PCA) is a popular dimension reduction technique for vector data. Factored PCA (FPCA) is a probabilistic extension of PCA for matrix data, which can substantially reduce the number of parameters in PCA while…

We study semiparametric factor models in high-dimensional panels where the factor loadings consist of a nonparametric component explained by observed covariates and an idiosyncratic component capturing unobserved heterogeneity. A key…

A general asymptotic framework is developed for studying consis- tency properties of principal component analysis (PCA). Our frame- work includes several previously studied domains of asymptotics as special cases and allows one to…

Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian…

In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…

Efficient representations of data are essential for processing, exploration, and human understanding, and Principal Component Analysis (PCA) is one of the most common dimensionality reduction techniques used for the analysis of large,…

Principal component analysis is a versatile tool to reduce dimensionality which has wide applications in statistics and machine learning. It is particularly useful for modeling data in high-dimensional scenarios where the number of…

Principal Component Analysis (PCA) is a well-known linear dimension-reduction technique designed for Euclidean data. In a wide spectrum of applied fields, however, it is common to observe multivariate circular data (also known as toroidal…

Data integration, or the strategic analysis of multiple sources of data simultaneously, can often lead to discoveries that may be hidden in individualistic analyses of a single data source. We develop a new unsupervised data integration…